A Dain Inequality with charge

We prove an upper bound for angular-momentum and charge in terms of the mass for electro-vacuum asymptotically flat axisymmetric initial data sets with simply connected orbit space

Sznajd Complex Networks

The Sznajd cellular automata corresponds to one of the simplest and yet most interesting models of complex systems. While the traditional two-dimensional Sznajd model tends to a consensus state (pro or cons), the assignment of the contrary to the dominant opinion to some of its cells during the system evolution is known to provide stabilizing feedback implying the overall system state to oscillate around null magnetization. The current article presents a novel type of geographic complex network model whose connections follow an associated feedbacked Sznajd model, i.e. the Sznajd dynamics is run over the network edges. Only connections not exceeding a maximum Euclidean distance $D$ are considered, and any two nodes within such a distance are randomly selected and, in case they are connected, all network nodes which are no further than $D$ are connected to them. In case they are not connected, all nodes within that distance are disconnected from them. Pairs of nodes are then randomly selected and assigned to the contrary of the dominant connectivity. The topology of the complex networks obtained by such a simple growth scheme, which are typically characterized by patches of connected communities, is analyzed both at global and individual levels in terms of a set of hierarchical measurements introduced recently. A series of interesting properties are identified and discussed comparatively to random and scale-free models with the same number of nodes and similar connectivity.Comment: 10 pages, 4 figure

Finding RR Lyrae Stars with SkyMapper: an Observational Test

One of the major science goals of the SkyMapper Survey of the Southern Hemisphere sky is the determination of the shape and extent of the halo of the Galaxy. In this paper we quantify the likely efficiency and completeness of the survey as regards the detection of RR Lyrae variable stars, which are excellent tracers of the halo stellar population. We have accomplished this via observations of the RR Lyrae-rich globular cluster NGC 3201. We find that for single epoch uvgri observations followed by two further epochs of g, r imaging, as per the intended three-epoch survey strategy, we recover known RR Lyraes with a completeness exceeding 90%. We also investigate boundaries in the gravity-sensitive single-epoch two-color diagram that yield high completeness and high efficiency (i.e., minimal contamination by non-RR Lyraes) and the general usefulness of this diagram in separating populations.Comment: 10 pages, 5 figures, to appear in the Publications of the Astronomical Society of Australia (PASA), published by Cambridge University Pres

Properties of Very Luminous Galaxies

Recent analysis of the SSRS2 data based on cell-counts and two-point correlation function has shown that very luminous galaxies are much more strongly clustered than fainter galaxies. In fact, the amplitude of the correlation function of very luminous galaxies ($L > L^*$) asymptotically approaches that of $R \ge 0$ clusters. In this paper we investigate the properties of the most luminous galaxies, with blue absolute magnitude $M_B \le -21$. We find that: 1) the population mix is comparable to that in other ranges of absolute magnitudes; 2) only a small fraction are located in bona fide clusters; 3) the bright galaxy-cluster cross-correlation function is significantly higher on large scales than that measured for fainter galaxies; 4) the correlation length of galaxies brighter than \MB $\sim -20.0$, expressed as a function of the mean interparticle distance, appears to follow the universal dimensionless correlation function found for clusters and radio galaxies; 5) a large fraction of the bright galaxies are in interacting pairs, others show evidence for tidal distortions, while some appear to be surrounded by faint satellite galaxies. We conclude that very luminous optical galaxies differ from the normal population of galaxies both in the clustering and other respects. We speculate that this population is highly biased tracers of mass, being associated to dark halos with masses more comparable to clusters than typical loose groups.Comment: 29 pages (6 figures) + 2 tables; paper with all figures and images available at http://boas5.bo.astro.it/~cappi/papers.html; The Astronomical Journal, in pres

Critical Behavior of a Three-State Potts Model on a Voronoi Lattice

We use the single-histogram technique to study the critical behavior of the three-state Potts model on a (random) Voronoi-Delaunay lattice with size ranging from 250 to 8000 sites. We consider the effect of an exponential decay of the interactions with the distance,$J(r)=J_0\exp(-ar)$, with $a>0$, and observe that this system seems to have critical exponents $\gamma$ and $\nu$ which are different from the respective exponents of the three-state Potts model on a regular square lattice. However, the ratio $\gamma/\nu$ remains essentially the same. We find numerical evidences (although not conclusive, due to the small range of system size) that the specific heat on this random system behaves as a power-law for $a=0$ and as a logarithmic divergence for $a=0.5$ and $a=1.0$Comment: 3 pages, 5 figure

Reconstruction of Quark Mass Matrices with Weak Basis Texture Zeroes from Experimental Input

All quark mass matrices with texture zeroes obtained through weak basis transformations are confronted with the experimental data. The reconstruction of the quark mass matrices M_u and M_d at the electroweak scale is performed in a weak basis where the matrices are Hermitian and have a maximum of three vanishing elements. The same procedure is also accomplished for the Yukawa coupling matrices at the grand unification scale in the context of the Standard Model and its minimal supersymmetric extension as well as of the two Higgs doublet model. The analysis of all viable power structures on the quark Yukawa coupling matrices that could naturally appear from a Froggatt-Nielsen mechanism is also presented.Comment: RevTeX4, 3 tables, 21 pages; misprints corrected and one reference adde